Unifying probabilistic and variational estimation

IEEE Signal Processing Magazine

Volumn 19, Issue 5, 2002, Pages 37-47

  Hamza, A Ben ^d   Krim, Hamid ^a,b   Unal, Gozde B ^a,c  

^a North Carolina State University   (United States)

^b IEEE

^c Information and Statistical Signal Theories and Applications Group

^d Information and Statistical Signal Theories and Applications Group ^*

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85032751811     PISSN: 10535888     EISSN: None     Source Type: Journal    
DOI: 10.1109/MSP.2002.1028351     Document Type: Article

References (24)

1. J. Astola and P. Kuosmanen, Fundamentals of Nonlinear Digital Filtering. Boca Raton, FL: CRC, 1997.
2. S. Geman and D. Geman, "Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images," IEEE Trans. Pattern Anal. Machine Intell., vol. 6, pp. 721-741, July 1984.
3. H. Stark, Ed., Image Recovery: Theory and Application. New York: Academic, 1987.
4. S.C. Zhu and D. Mumford, "Prior learning and Gibbs reaction-diffusion," IEEE Trans. Pattern Anal. Machine Intell., vol. 19, pp. 1236-1244, Nov. 1997.
5. P. Perona and J. Malik, "Scale space and edge detection using anisotropic diffusion," IEEE Trans. Pattern Anal. Machine Intell., vol. 12, pp. 629-639, July 1990.
6. L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D, vol. 60, pp. 259-268, 1992.
7. D. Tschumperle and R. Deriche, "Diffusion PDEs on vector-valued images," IEEE Signal Processing Mag., vol. 19, pp. 16-25, Sept. 2002.
8. I. Pollak, "Segmentation and restoration via nonlinear multiscale filtering," IEEE Signal Processing Mag., vol. 19, pp. 26-36, Sept. 2002.
9. H. Krim and I.C. Schick, "Minimax description length for signal denoising and optimized representation," IEEE Trans. Inform. Theory, vol. 45, pp. 898-908, Apr. 1999.
10. I. Pollak, A.S. Willsky, and H. Krim, "Image segmentation and edge enhancement with stabilized inverse diffusion equations," IEEE Trans. Image Processing, vol. 9, pp. 256-266, Feb. 2000.
11. J. Morel and S. Solemini, Variational Methods in Image Segmentation. Boston, MA: Birkhaüser, 1995.
12. C. Samson, L. Blanc-Feraud, G. Aubert, and J. Zerubia, "A variational model for image classification and restoration," IEEE Trans. Pattern Anal. Machine Intell., vol. 22, pp. 460-472, May 2000.
13. M. Giaquinta and S. Hildebrandt, Calculus of Variations I: The Lagrangian Formalism. New York: Springer-Verlag, 1996.
14. A. Chambolle and P.L. Lions, "Image recovery via total variation minimization and related problems," Num. Math., vol. 76, pp. 167-188, 1997.
15. K. Ito and K. Kunisch, "Restoration of edge-flat-grey scale images," Inverse Problems, vol. 16, no. 4, pp. 909-928, Aug. 2000.
16. Y.L. You, W. Xu, A. Tannenbaum, and M. Kaveh, "Behavioral analysis of anisotropic diffusion in image processing," IEEE Trans. Image Processing, vol. 5, pp. 1539-1553, Nov. 1996.
17. P. Huber, Robust Statistics. New York: Wiley, 1981.
18. M.J. Black, G. Sapiro, D. H. Marimont, and D. Heeger, "Robust anisotropic diffusion," IEEE Trans. Image Processing, vol. 7, pp. 421-432, Mar. 1998.
19. H. Krim, "On the distributions of optimized multiscale representations," ICASSP-97, vol. 5, pp. 3673 -3676, 1997.
20. A. Ben Hamza and H. Krim, "A variational approach to maximum a posteriori estimation For Image denoising," Lecture Notes in Comput. Sci., vol. 2134, pp. 19-34, Sept. 2001.
21. A. Ben Hamza and H. Krim, "Image denoising: A nonlinear robust statistical approach," IEEE Trans. Signal Processing, vol. 49, pp. 3045-3054, Dec. 2001.
22. H. Krim and Y. Bao, "Smart nonlinear diffusion: A probabilistic approach," submitted for publication.
23. M.A. Grayson, "The heat equation shrinks embedded plane curves to round points," J. Differ. Geometry, vol. 26, pp. 285-314, 1987.
24. G.B. Unal, H. Krim, A. Yezzi, "Stochastic differential equations and geometric flows," IEEE Trans. Image Processing, to be published.